In testing, updates worked correctly. However, some users with specific settings or extensions may need to reset their settings since there are major changes from 3.2.0 to 4.1.1. You can delete the Data directory within the OpenOfficePortable directory to reset your settings. Or delete the whole folder and install fresh to ensure you have a perfectly clean version.

OpenOffice Portable didn't have many testers and the existing 3.2.0 release didn't have many users any longer as most folks have long since switched to LibreOffice Portable by now.

OpenOffice 3.2.0 is insecure and unsupported. It should not be used any longer.

As for how they're related and compare, some backstory helps. OpenOffice as a project basically died about 4 years ago when Oracle acquired it and let it stagnate. That's also when they revoked permission for any portable versions at all. Most of the OpenOffice developers left and formed The Document Foundation and continued OpenOffice development as LibreOffice. They couldn't continue to call it OpenOffice as Oracle owned the trademarks and refused to let The Document Foundation use them. Later, Oracle realized it was a dead project and gifted it (including the trademarks) to the Apache Foundation who restarted development. The new team spent a lot of time redeveloping sections of OpenOffice so they could re-license it under the Apache license instead of the GPL/LGPL. OpenOffice is still being developed but at a slower pace than LibreOffice. LibreOffice has more features than OpenOffice due to the additional development time spent on it, the larger development team, and the fact that OpenOffice spent time redeveloping existing features for licensing reasons. LibreOffice also does more releases faster, which can sometimes introduce bugs. That's why they offer a "Fresh" and a "Still" branch, depending on your needs.

As for what you should use, I'd suggest trying them both. They are very similar in interface and base features. LibreOffice has better Microsoft Office compatibility, but most docs and spreadsheets will work in both. LibreOffice is a much smaller install than OpenOffice. Lots of people prefer LibreOffice, lots of people prefer OpenOffice. Rename your existing OpenOfficePortable folder to OpenOfficePortableOld so you can keep it as well if you'd like.